ADAPTIVE AND ROBUST CONTROLS FOR UNCERTAIN LINEAR AND NONLINEAR SYSTEMS By JUNG E. SON A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy ADAPTIVE AND ROBUST CONTROLS FOR UNCERTAIN LINEAR AND NONLINEAR SYSTEMS By Jung E. Son August 2012 Chair: Haniph A. Latchman Cochair: Pramod P. Khargonekar Major: Electrical and Computer Engineering The presence of various uncertainties in control systems is one of the main challenging issues to engineers since this problem in real applications gives rise to instability and degradation of performance. This dissertation addresses analysis and control design problems involving linear and nonlinear systems with structured and unstructured uncertainties. In the first problem, the critical direction theory (CDT) an H∞ design is proposed as a systematic controller synthesis methodology for a linear system with parametric uncertainties. In the literature, a significant conservatism issue in this study of such uncertain systems with respect to robust control design has been reported. First, the mechanisms leading to conservatism in an earlier approach utilizing a constant overbounding uncertainty template are analyzed. Then, motivated by the desire to decrease the conservative uncertainty, a static weight approach based on the CDT is examined using a constant value to describe the uncertainties over all frequencies. This approach shows that the CDT combined with H∞ is effective and promising for less conservative stability and controller synthesis for a linear system with uncertainties. The second is a study of the problem of the robustness of multi-input multi-output (MIMO) systems with parametric uncertainties. Two criteria that are used to assess the